Calculation method for earth pressure on vertical arms of multi-level cantilever walls

Abstract

The present invention discloses a calculation method for the earth pressure on the vertical wall of a multi-level cantilever wall, which can reasonably reflect the failure mode of the multi-level cantilever wall and has a simple solution process. The method includes the following steps: Step 100, establishing an expression for the resultant earth pressure on the back of the calculation wall; Step 200, calculating the resultant earth pressure on the back of the calculation wall, its included angle with the vertical direction, and the horizontal inclination angle of the overall rupture surface in the soil mass behind the wall; Step 300, calculating the resultant earth pressure on each local secondary rupture surface and the horizontal inclination angle of each local secondary rupture surface; Step 400, for the sliding soil wedge, using the horizontal strip method to calculate the normal stress and shear stress on each local secondary rupture surface, and performing resultant force equivalent correction according to the resultant earth pressure on each local secondary rupture surface; Step 500, for the unit soil mass, using the horizontal strip method with the same number of strips as the corresponding sliding soil wedge to calculate the earth pressure distribution on the vertical wall of each level of the cantilever wall; Step 600, calculating the resultant earth pressure on the vertical wall of the corresponding level of the cantilever wall.

Description

Technical Field

[0001] The present invention relates to the technical field of geotechnical foundation engineering, and particularly relates to a calculation method for the earth pressure on the vertical wall of a multi-level cantilever wall. Background Art

[0002] Cantilever retaining walls (simply referred to as cantilever walls) have the advantages of light self-weight and good seismic performance, and have received extensive attention in geotechnical retaining engineering. Cantilever walls include two types: single-level and multi-level. Among them, multi-level cantilever walls are more complex in structure than single-level cantilever walls and are applicable to more complex retaining projects.

[0003] At present, the numerical simulation method is a general method for analyzing the earth pressure problem of cantilever walls. However, due to the difficulty of professional operation and the time-consuming calculation process, it is difficult to be widely promoted in practice. In order to simplify the earth pressure problem of cantilever walls, in practice, some approximate algorithms based on Coulomb and Rankine earth pressure theories are mostly used to calculate the active earth pressure on the imaginary retaining wall on the back of a single-level cantilever wall. However, such methods cannot obtain the earth pressure distribution on the vertical wall, and the earth pressure distribution on the vertical wall is an important basis for the structural design of the cantilever retaining wall. In particular, different from single-level cantilever walls, multi-level cantilever walls are a new type of retaining structure, and there are few reports on the calculation method for the earth pressure on the vertical wall of multi-level cantilever walls. In fact, for multi-level cantilever walls, in addition to the overall rupture surface in the soil mass behind the wall, some model tests and numerical simulations show that there are local secondary rupture surfaces above the heel plates of each level of multi-level cantilever walls, and the local secondary rupture surfaces have an impact on the earth pressure distribution on the vertical wall of the cantilever wall, but there is a lack of relevant consideration and analysis in the previous calculation methods for earth pressure. Summary of the Invention

[0004] The purpose of the present invention is to make up for the deficiency that the existing technology cannot reasonably calculate the earth pressure on the vertical wall of a multi-level cantilever wall, and to propose a calculation method for the earth pressure on the vertical wall of a multi-level cantilever wall that can reasonably reflect the failure mode of the multi-level cantilever wall and has a simplified solution process.

[0005] In order to achieve the above-mentioned invention purpose, the technical solution of the calculation method for the earth pressure on the vertical wall of the multi-level cantilever wall provided by the present invention is as follows:

[0006] A calculation method for the earth pressure on the vertical wall of a multi-level cantilever wall, the cantilever wall includes a vertical wall and a bottom plate, and the bottom plate located in the soil mass behind the vertical wall is a heel plate. The calculation method mainly includes the following steps:

[0007] Step 100, establish an expression for the resultant earth pressure on the calculation back wall in the soil mass behind the multi-level cantilever wall; the soil mass behind the wall is surrounded by each level of cantilever wall and the overall rupture surface; the calculation back wall is continuously formed by the local secondary rupture surfaces on the rear sides of the cantilever walls of each level and the local bottom segments of the heel plates of each level of cantilever wall;

[0008] Step 200: Calculate the resultant earth pressure acting on the soil mass behind the wall on the calculated back surface of the wall, the angle between the resultant earth pressure on the calculated back surface of the wall and the vertical direction, and the horizontal inclination angle of the overall failure surface in the soil mass behind the wall accordingly.

[0009] Step 300: Calculate the resultant earth pressure on each local secondary failure surface from top to bottom of the multi - level cantilever wall and the horizontal inclination angle of each local secondary failure surface.

[0010] Step 400: For the sliding soil wedge jointly enclosed by the overall failure surface, the calculated back surface of the wall, and the slope top, use the horizontal strip - division method to calculate the normal stress and shear stress on each local secondary failure surface, and perform a resultant force equivalent correction on the normal stress and shear stress of its corresponding section according to the resultant earth pressure on each local secondary failure surface.

[0011] Step 500: According to the normal stress and shear stress on each local secondary failure surface, for the unit soil mass enclosed by each local secondary failure surface and the vertical wall of the same - level cantilever wall, use the horizontal strip - division method with the same number of strips as the corresponding sliding soil wedge to calculate the earth pressure distribution on the vertical wall of each level of the cantilever wall.

[0012] Step 600: Calculate the resultant earth pressure on the vertical wall of the corresponding level of the cantilever wall according to the earth pressure distribution on the vertical wall of each level of the cantilever wall.

[0013] The present invention focuses on the actual failure mode of the soil mass behind the multi - level cantilever wall retaining structure, establishes a mechanical analysis model that includes both the overall failure surface and local secondary failure surfaces, and finally solves the earth pressure distribution on the vertical wall through force transfer. By using a mathematical optimization solution method to determine the positions of the overall failure surface and local secondary failure surfaces, the solution idea is not only convenient for actual operation but also can reasonably reflect the failure mode of the multi - level cantilever wall, realizing the rapid solution of the earth pressure on the vertical wall of the multi - level cantilever wall, and its technical method significance and practical value are remarkable.

[0014] The following further describes the present invention in conjunction with the accompanying drawings and specific embodiments. The additional aspects and advantages of the present invention will be partially given in the following description, partially become obvious from the following description, or be understood through the practice of the present invention. Brief Description of the Drawings

[0015] The accompanying drawings constituting a part of the present invention are used to assist in understanding the present invention. The content provided in the accompanying drawings and the related description in the present invention can be used to explain the present invention, but do not constitute an improper limitation to the present invention.

[0016] Figure 1 It is a schematic structural diagram of the cantilever wall of the present invention.

[0017] Figure 2 It is a diagram of the active ultimate failure mode of the soil mass behind the multi - level cantilever wall of the present invention.

[0018] Figure 3 It is a diagram of the strip division method of the soil mass behind the multi - level cantilever wall of the present invention.

[0019] Figure 4 It is a schematic structural diagram of the embankment slope supported by a three - level cantilever wall according to an embodiment of the present invention.

[0020] Figure 5 It is a diagram of the earth pressure distribution of the vertical wall of the three - level cantilever wall under static conditions according to an embodiment of the present invention.

[0021] Figure 6 It is a diagram of the earth pressure distribution of the vertical wall of the three - level cantilever wall under seismic conditions according to an embodiment of the present invention.

[0022] The relevant markings in the above - mentioned drawings are: 100 - overall rupture surface, 200 - local secondary rupture surface, 300 - sliding soil wedge, 400 - unit soil mass, 500 - slope top. Specific Embodiments

[0023] The specific embodiments of the calculation method of the earth pressure on the vertical wall of the multi - level cantilever wall of the present invention include the following steps:

[0024] Step 100: Establish an expression for the resultant earth pressure on the back of the wall in the soil mass behind the multi - level cantilever wall.

[0025] Figure 1 It is a schematic structural diagram of the cantilever wall. As Figure 1 shown, the cantilever wall includes a vertical wall and a base plate. The base plate located in the soil mass behind the vertical wall is the heel plate.

[0026] Based on the Coulomb earth pressure assumption and using the plane mode, the active ultimate failure mode of the soil mass behind the multi - level cantilever wall is obtained as Figure 3 shown. In Figure 3 , the soil mass behind the wall is enclosed by each level of the cantilever wall and the overall rupture surface 100. The calculated back of the wall is continuously formed by the local secondary rupture surfaces 200 (i.e., the surfaces where BC, DE, and FG are located) on the back side of each level of the cantilever wall and the local bottom segments of the heel plates of each level of the cantilever wall (i.e., the surface where the line segment BCDEFG is located). The sliding soil wedge 300 behind the wall is jointly enclosed by the overall rupture surface 100, the calculated back of the wall, and the slope top 500 (i.e., the area enclosed by the line ABCDEFGA).

[0027] Establish an overall mechanical equilibrium equation set for the sliding soil wedge 300, as shown in Equations (1) and (2), and then derive an expression for the resultant earth pressure acting on the calculated back of the wall, as shown in Equation (3).

[0028]

[0029]

[0030]

[0031] Among them, E represents the resultant earth pressure on the back of the wall; β represents the angle between the resultant earth pressure on the back of the wall and the vertical direction. k h represents the horizontal seismic influence coefficient; k v represents the vertical seismic influence coefficient; M represents the gravity of the sliding soil wedge 300; R represents the reaction force on the overall rupture surface 100; θ represents the horizontal inclination angle of the overall rupture surface 100, and θ satisfies d is the length of the sole plate of a single-stage cantilever wall, b is the length of the heel plate of a single-stage cantilever wall, w is the horizontal offset distance between two adjacent upper and lower single-stage cantilever walls, and H 2 is the net wall height of the k-th (k > 1) cantilever wall from top to bottom; represents the internal friction angle of the soil behind the wall; q represents the uniformly distributed load at the slope top 500; l represents the length of the sliding soil wedge 300 at the slope top 500 (i.e., the length of line segment AB); n is the total number of multi-stage cantilever walls from top to bottom; P k is the partial base pressure of the k-th cantilever wall from top to bottom within the sliding soil wedge 300. According to the total vertical pressure at the bottom of the heel plate of each cantilever wall (equal to the superposition of the upper cantilever wall, fill soil, and slope load), P is calculated by distributing according to the proportion of the base width of this section to the total width of the corresponding heel plate. k .

[0032] Taking a three-stage wall as an example, that is, when n = 3, the expressions of M and P k are respectively:

[0033]

[0034]

[0035]

[0036] Among them, γ s is the unit weight of the soil behind the wall; γ w is the unit weight of the cantilever wall; H is the total height of the three-stage cantilever wall; H 1 is the total height of the first-stage cantilever wall; H 2 is the net wall height of the k-th cantilever wall, and the net wall heights of each level (k > 1) of the cantilever wall are equal. The net wall height is the vertical distance between the bottom surface of the sole plate of this level of the cantilever wall and the bottom surface of the sole plate of the upper-level cantilever wall; α is the horizontal inclination angle of each local secondary rupture surface 200; L 1 and L 2 are the lengths of line segments CD and EF respectively; t is the thickness of the sole plate of the cantilever wall; S w is the cross-sectional area of a single-stage cantilever wall.

[0037] Step 200: Calculate the resultant earth pressure acting on the back of the wall in the soil mass behind the wall, the angle between the resultant earth pressure acting on the back of the wall and the vertical direction, and the horizontal inclination angle of the overall failure surface 100 in the soil mass behind the wall accordingly.

[0038] Calculate the corresponding β by using the method of finding the minimum anti-sliding stability coefficient of the entire multi-level cantilever wall along the bottom slab of the lowest-level cantilever wall. 0 and θ 0 , and their values are the solutions of β and θ in the expression shown in Equation (4).

[0039]

[0040] where K s is the anti-sliding stability coefficient of the entire multi-level cantilever wall along the bottom slab of the lowest-level cantilever wall, and its expression is:

[0041]

[0042] where W S is the sum of the self-weight of the unit soil mass 400 and the self-weights of each level of cantilever walls; f is the friction coefficient between the bottom slab of the lowest-level cantilever wall and the foundation.

[0043] Substitute the solution β of β calculated according to Equation (4) 0 and the solution θ of θ 0 into Equation (3), and the corresponding resultant earth pressure value E on the back of the calculated wall can be determined. R .

[0044] Step 300: Calculate the resultant earth pressure on each level of local rupture surface 200 from top to bottom of the multi-level cantilever wall and the horizontal inclination angle of each level of local rupture surface 200.

[0045] According to the general relationship that the earth pressure is positively correlated with the square of the wall height, the proportional relationship that can be adopted between the resultant earth pressures on each level of local rupture surface 200 from top to bottom is:

[0046]

[0047] Meanwhile, through some test and numerical simulation results, it is obtained that the inclination angles of each level of local rupture surface 200 are close. For the sake of simplified analysis, the present invention adopts the method that the inclination angles of each level of local rupture surface 200 are equal, that is, the horizontal inclination angle of each level of local rupture surface 200 from top to bottom is α, and its expression is:

[0048]

[0049] where α is the horizontal inclination angle of each level of local rupture surface 200; β 0 is the solution of β; π is the pi.

[0050] Thus, based on the resultant value E of the earth pressure on the calculation wall surface that has been solved R , according to the equivalent principle of the resultant earth pressure on the calculation wall surface, we can obtain:

[0051]

[0052] Among them, E 1 and E k respectively represent the earth pressures on the 1st and kth (k > 1) local split surfaces 200 from top to bottom; E R is the solution of the earth pressure on the calculation wall surface; h q is the equivalent soil column height of the uniform load q at the slope top 500, which is equal to q divided by the unit weight of the soil behind the wall.

[0053] Step 400: For the sliding soil wedge 300, use the horizontal slice method to calculate the normal stress and shear stress on each level of the local split surface 200, and perform a resultant equivalent correction on the normal stress and shear stress of its corresponding section according to the resultant earth pressure on each level of the local split surface 200.

[0054] For the sliding soil wedge 300 behind the wall, use the horizontal slice method to calculate the normal stress and shear stress on each level of the local split surface 200 before correction and their corresponding resultant earth pressures, and their calculation expressions are:

[0055]

[0056] Among them, according to the Mohr-Coulomb strength criterion, we have:

[0057]

[0058] Therefore, according to the equivalent principle of the resultant earth pressure on each level of the local split surface 200, correct the normal stress and shear stress calculated by the horizontal slice method, and the calculation expression of the correction coefficient is:

[0059]

[0060] Thus, the normal stress and shear stress on the corresponding local split surface 200 of the ith soil strip after correction are respectively:

[0061]

[0062] Among them, p i and t i respectively represent the normal stress and shear stress corresponding to the ith soil strip on each level of the local split surface 200 before correction, p j and t jrespectively represent the normal and tangential stresses corresponding to the \(i\)-th soil strip on the modified local secondary fracture surface 200 at all levels. The subscript \(i\) represents the serial number of the soil strip from top to bottom after horizontally dividing the sliding soil wedge 300; \(z\) i is the length intercepted by the \(i\)-th strip on the local secondary fracture surface 200, and there is \(h\) i is the thickness of the \(i\)-th soil strip; \(W\) i is the self-weight of the \(i\)-th soil strip, and there is \(N\) i and \(T\) i are respectively the normal and tangential forces on the overall fracture surface 100 corresponding to the \(i\)-th strip; \(Q\) i-1 and \(Q\) i are respectively the vertical inter-strip forces on the top and bottom surfaces of the \(i\)-th strip; \(l\) i-1 and \(l\) i are the lengths of the top and bottom surfaces of the \(i\)-th strip; \(\xi\) is the correction coefficient; \(m\) is the total number of strips.

[0063] Step 500: According to the normal stress and tangential stress on the local secondary fracture surface 200 at all levels, for each level of unit soil mass 400, adopt the horizontal strip method with the same number of strips as that of the corresponding sliding soil wedge 300 to calculate the earth pressure distribution on the vertical wall of each level of cantilever wall.

[0064] For each level of unit soil mass 400, adopting the horizontal strip method with part of the same number of strips as that of the corresponding sliding soil wedge 300, from the mechanical equilibrium conditions of each soil strip, we can obtain:[[]]

[0065]

[0066] Among them, \(h\) j is the thickness of the \(j\)-th soil strip; \(j\) is the serial number of the strip from top to bottom when horizontally dividing the unit soil mass 400, \(1\leq j\leq m\), and its strip division method is consistent with that of the corresponding sliding soil wedge 300; \(\sigma\) j and \(\tau\) j are respectively the normal stress and tangential stress acting on the vertical wall of the cantilever wall; \(F\) j-1 and \(F\) j are respectively the vertical inter-strip forces on the top and bottom surfaces of the \(j\)-th strip; \(W\) j is the self-weight of the \(j\)-th soil strip; \(l\) j-1 and \(l\) j are the lengths of the top and bottom surfaces of the \(j\)-th strip.

[0067] By solving the system of equations (11) for each soil strip from top to bottom, the normal stress and tangential stress on the vertical wall of each level of cantilever wall can be obtained, that is, its earth pressure distribution is determined.

[0068] Step 600: According to the earth pressure distribution on the vertical wall of each level of cantilever wall, calculate the resultant earth pressure on the vertical wall of the corresponding level of cantilever wall.

[0069] After calculating the normal stress and shear stress on the vertical arms of each level of the cantilever wall, the resultant earth pressure on the vertical arms of the corresponding levels of the cantilever wall can be obtained, and its calculation expression is:

[0070]

[0071] Among them, E wk is the resultant earth pressure on the vertical arm of the k-th level of the cantilever wall, and m k is the total number of horizontal strips of the k-th unit soil mass 400400.

[0072] The beneficial effects of the present invention will be described below through specific embodiments.

[0073] Figure 4 It is a schematic structural diagram of the actual embankment slope supported by a three-level cantilever wall in the embodiment of the present invention. The concrete material of the cantilever wall is C35 concrete. The sizes of each level of the cantilever wall are the same. The soil mass behind the wall is backfilled and compacted with coarse sand. The relevant parameters are shown in Table 1.

[0074] Table 1

[0075]

[0076] The following describes the method of the present invention for solving the earth pressure distribution and its resultant force acting on the vertical arms of each level of the cantilever wall under the static condition (k h = 0; k v = 0) and the seismic condition (k h = 0.1; k v = 0.05).

[0077] I. Static condition

[0078] Step 100: According to Equation (3), the expression for calculating the resultant earth pressure on the back of the wall is:

[0079]

[0080] Step 200: Substitute Equation (13) into Equation (4a), and then solve according to Equation (4) to obtain the resultant earth pressure on the back of the wall and the vertical angle β 0 = 48.21°, the horizontal inclination angle θ 0 of the overall rupture surface 100 = 60.71°; then substitute β 0 and θ 0 into Equation (13) to obtain the resultant earth pressure E R on the back of the wall = 175.655 kN / m.

[0081] Step 300: According to Equation (6), it can be obtained:

[0082]

[0083] According to Equation (7), α = 96.79°.

[0084] Step 400: As Figure 3 shown, for the sliding soil wedge 300, the number of horizontal sub - strips corresponding to the corresponding part of the vertical wall of each - level cantilever wall is taken as 5, and 1 sub - strip is taken at the heel plate. The total number of horizontal sub - strips m of the three - level cantilever wall = (5 + 1)×3 = 18.

[0085] According to Equation (8), the normal stress p i and shear stress t i on the local secondary rupture surface 200 of each soil strip can be recursively calculated from top to bottom, and thus the soil pressure correction coefficient ξ = 0.972 can be solved according to Equation (9).

[0086] Step 500: As Figure 3 shown, for each - level unit soil mass 400, the normal stress σ j and shear stress τ j on the vertical wall of each level can be recursively calculated from top to bottom according to Equations (10) and (11), and thus the soil pressure distribution on the vertical wall of each level can be determined as Figure 5 shown.

[0087] Step 600: According to Equation (12), the resultant soil pressures on the vertical walls of the cantilever walls of each level from top to bottom can be calculated as follows:

[0088] E w1 = 27.7 kN / m

[0089] E w2 = 50.6 kN / m

[0090] E w3 = 70.3 kN / m

[0091] II. Earthquake condition

[0092] Step 100: According to Equation (3), the expression for calculating the resultant soil pressure on the back of the wall is:

[0093]

[0094] Step 200: Substitute Equation (14) into Equation (4a), and then solve according to Equation (4) to obtain the included angle β 0 = 49.37° between the resultant soil pressure on the back of the wall and the vertical direction, and the horizontal inclination angle θ 0 = 57.63° of the overall rupture surface 100; then substitute β 0 and θ 0 into Equation (14) to obtain the resultant soil pressure E R= 189.649 kN / m.

[0095] Step 300: According to Equation (6), it can be obtained that:

[0096]

[0097] According to Equation (7), α = 95.63°.

[0098] Step 400: For the sliding soil wedge 300, the number of horizontal sub - strips corresponding to the corresponding parts of the vertical arms of each - level cantilever wall is taken as 5, and 1 sub - strip is taken at the heel plate. The total number of horizontal sub - strips of the three - level cantilever wall m=(5 + 1)×3 = 18.

[0099] According to Equation (8), the normal stress p i and shear stress t i on the local two - fracture plane 200 of each soil strip can be recursively calculated from top to bottom, and thus the soil pressure correction coefficient ξ = 0.985 can be solved according to Equation (9).

[0100] Step 500: For each - level unit soil body 400, the normal stress σ j and shear stress τ j on each - level vertical arm can be recursively calculated from top to bottom according to Equations (10) and (11), and thus the soil pressure distribution on each - level vertical arm can be determined as Figure 6 shown.

[0101] Step 600: According to Equation (12), the resultant soil pressures on the vertical arms of each - level cantilever wall from top to bottom can be calculated as follows:

[0102] E w1 = 31.3 kN / m

[0103] E w2 = 55.3 kN / m

[0104] E w3 = 76.0 kN / m

[0105] III. Result Comparison

[0106] Under the static condition, the resultant soil pressures on the vertical arms of each - level calculated by the method of the present invention from top to bottom are 27.7, 50.6, 70.3 kN / m respectively, and the corresponding calculation results by the FLAC3D numerical simulation method are 30.93, 51.75, 71.35 kN / m respectively. The absolute value of the maximum relative error is about 10%.

[0107] Under seismic conditions, the resultant earth pressures on the vertical arms at each level from top to bottom calculated by the method of the present invention are 31.3, 55.3, and 76.0 kN / m respectively, and the corresponding calculation results by the FLAC3D numerical simulation method are 35.58, 59.35, and 80.40 kN / m. The absolute value of the maximum relative error is approximately 12%.

[0108] As Figures 5 - 6 shown, under the two working conditions of static and seismic conditions, the earth pressures on the vertical arms at each level of the method of the present invention and the FLAC3D numerical simulation method are relatively consistent in the overall distribution pattern. These results indicate the rationality of the calculation method of the present invention.

[0109] The calculation method of the earth pressure on the vertical arms of the multi-level cantilever wall of the present invention has the following advantages:

[0110] First, the failure mode of the analysis model of the present invention simultaneously considers the overall global rupture surface 100 and the local multi-level distributed local secondary fracture surfaces 200. This failure mode can reasonably reflect the actual situation.

[0111] Secondly, the mechanical concept of the present invention is clear and the principle is concise. According to the method that the anti-sliding stability coefficient of the bottommost cantilever wall floor along the entire multi-level cantilever wall is the smallest, the resultant earth pressure on the calculation wall surface, its vertical inclination angle, and the position of the global rupture surface 100 are determined. Then, the earth pressure distribution on the local secondary fracture surface 200 is determined by horizontal slicing of the sliding soil wedge 300, and the normal and tangential stress results of the horizontal slicing method are corrected according to the resultant earth pressure equivalence principle. Then, the soil mass enclosed between each level of the wall vertical arm and the local secondary fracture surface 200 is horizontally sliced again, and the earth pressure distribution and its resultant force acting on each level of the cantilever wall vertical arm can be determined.

[0112] Finally, the calculation process of the method of the present invention is simple, easy to operate, the calculation results are relatively accurate, and the earth pressure under static and seismic conditions can be calculated simultaneously.

[0113] It can be seen that the calculation method of the earth pressure on the vertical arms of the multi-level cantilever wall of the present invention reasonably considers the failure mode of the multi-level cantilever wall, takes into account both static and seismic conditions, has a clear calculation principle, a simple and easy-to-operate calculation process, relatively accurate calculation results, avoids the complex modeling analysis steps and time-consuming calculation process of the numerical simulation method, not only reasonably reflects the instability failure mode of the multi-level cantilever wall, but also has a simplified solution process, providing a convenient and effective method for the engineering design of such multi-level cantilever wall retaining structures, taking into account both technical significance and engineering practical value.

[0114] The above describes the relevant content of the present invention. Those of ordinary skill in the art will be able to implement the present invention based on these descriptions. Based on the above content of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present invention.

Claims

1. A method for calculating the earth pressure of a multi-stage cantilever wall vertical arm. The cantilever wall includes a vertical arm and a bottom plate. The bottom plate located in the soil behind the vertical arm is a heel plate. The method is characterized by: The calculation method mainly includes the following steps: Step 100, establishing an expression for the resultant earth pressure on the back side of the calculated wall in the soil behind the wall along the multi-stage cantilever wall; the soil behind the wall is surrounded by the cantilever walls at each stage and the overall fracture surface (100); the back side of the calculated wall is continuously composed of the local two-crack surface (200) on the back side of the cantilever wall of each stage and the local bottom surface section of the heel plate of each stage; Step 200, calculating the resultant earth pressure acting on the back of the wall in the soil behind the wall, the angle between the resultant earth pressure on the back of the wall and the vertical direction, and the horizontal inclination angle of the overall fracture surface (100) in the soil behind the wall; Step 300, calculating the resultant earth pressure on each level of the local two-split surface (200) from top to bottom of the multi-level cantilever wall and the horizontal inclination angle of each level of the local two-split surface (200); Step 400, for the sliding soil wedge (300) surrounded by the overall fracture surface (100), the back of the calculation wall and the top of the slope (500), the normal stress and the tangential stress on each level of the local two-cleft surface (200) are calculated by the horizontal strip method, and the normal stress and the tangential stress of the corresponding section are corrected by the resultant force of the soil pressure on each level of the local two-cleft surface (200); Step 500, based on the normal stress and tangential stress on the local bifurcation surface (200) of each level, for the unit soil body (400) enclosed between the local bifurcation surface (200) of each level and the cantilever wall vertical arm of the same level, the soil pressure distribution on the cantilever wall vertical arm of each level is calculated by using the horizontal strip division method with the same number of strip divisions as the corresponding sliding soil wedge (300); Step 600, according to the soil pressure distribution on the cantilever wall vertical arms of each level, calculate the soil pressure resultant on the cantilever wall vertical arms of the corresponding level; In step 100, the expression for calculating the resultant earth pressure on the back of the wall is: Where E represents the resultant earth pressure on the back of the wall; k h represents the horizontal earthquake influence coefficient; k v represents the vertical earthquake influence coefficient; M represents the gravity of the sliding soil wedge (300); q represents the uniformly distributed load on the top of the slope (500); l represents the length of the sliding soil wedge (300) at the top of the slope (500); P k is the base pressure of a portion of the k-th cantilever wall from top to bottom within the sliding soil wedge (300); n is the total number of multiple cantilever walls from top to bottom; represents the internal friction angle of the soil behind the wall; β represents the angle between the resultant earth pressure on the back of the wall and the vertical direction. θ represents the horizontal inclination angle of the overall fracture surface (100), and θ satisfies d is the length of the bottom plate of a single-stage cantilever wall, b is the length of the heel plate of a single-stage cantilever wall, w is the horizontal offset distance between the two adjacent cantilever walls, H2 is the clear wall height of the kth cantilever wall from top to bottom, k>1; In step 300, according to the equivalent principle of calculating the resultant earth pressure on the back of the wall, the calculation expression of the resultant earth pressure on each level of local two-split surface (200) is obtained as follows: Among them, E1 and E k They represent the soil pressure on the 1st and kth local split planes (200) from top to bottom, respectively, k>1; E R is the solution for calculating the resultant earth pressure on the back of the wall; H1 is the total height of the first-level cantilever wall; H2 is the net wall height of the k-th level cantilever wall, k>1, and the net wall heights of each level of cantilever wall are equal. The net wall height is the vertical distance between the bottom surface of the bottom plate of the cantilever wall of this level and the bottom surface of the bottom plate of the cantilever wall of the previous level; h q It is the equivalent soil column height of the uniformly distributed load q at the top of the slope (500), which is equal to q divided by the weight of the soil behind the wall.

2. The method for calculating the earth pressure of the multi-stage cantilever wall according to claim 1, characterized in that: The overall fracture surface (100) and the local two-crack surfaces (200) at various levels are all planar sliding surfaces.

3. The method for calculating the earth pressure of the multi-stage cantilever wall stand as claimed in claim 2, characterized in that: In step 200, the angle between the back of the wall and the vertical direction and the horizontal inclination angle of the overall fracture surface (100) are calculated, and are determined by solving the method of minimizing the anti-sliding stability coefficient along the bottom plate of the lowest level cantilever wall, and the expression satisfied is: Among them, K s is the anti-sliding stability coefficient of the entire multi-level cantilever wall along the bottom plate of the lowest level cantilever wall, and its expression is: Among them, W S is the sum of the self-weight of the unit soil (400) and the self-weight of each level of cantilever walls; f is the friction coefficient between the bottom plate of the lowest level cantilever wall and the foundation.

4. The method for calculating the earth pressure of the multi-stage cantilever wall stand as claimed in claim 3, characterized in that: In step 300, the horizontal inclination angles of the local bifurcation planes (200) at each level are the same, and the expression is: Among them, α is the horizontal inclination angle of the local bifurcation plane (200) at each level; β0 is the solution of β; π is pi.

5. The method for calculating the earth pressure of the multi-stage cantilever wall stand as claimed in claim 4, characterized in that: In step 400, the expressions of normal stress and tangential stress of each level of local bifurcation surface (200) before correction are: According to the principle of equivalence of the earth pressure resultant of each level of local two-crack surface (200), the normal stress and tangential stress calculated by the horizontal strip method are corrected. The expression of the correction coefficient is: The normal and tangential stresses on the local bifurcation plane (200) corresponding to the corrected i-th soil strip are: Among them, p i and t i They represent the normal stress and tangential stress corresponding to the ith soil strip on each level of the local two-crack surface (200) before correction, respectively. j and t j They represent the normal and tangential stresses corresponding to the i-th soil strip on each level of the local bifurcation surface (200) after correction, respectively. The subscript i represents the soil strip number from top to bottom after the sliding soil wedge (300) is horizontally divided into strips; z i is the length of the bar i corresponding to the interception on the local bifurcation plane (200), h i is the thickness of the i-th soil strip; W i is the self-weight of the i-th soil strip, N i and T i are the normal and tangential forces on the corresponding overall fracture surface (100) of the i-th strip, respectively; Q i-1 and Q i are the vertical inter-strip forces on the top and bottom surfaces of the i-th strip, respectively; l i-1 and l i is the length between the top and bottom of the i-th block; ξ is the correction coefficient; m is the total number of strips.

6. The method for calculating the earth pressure of the multi-stage cantilever wall stand as claimed in claim 5, characterized in that: In step 500, the expression for the distribution of earth pressure on each level of cantilever wall vertical arm is: σ j h j -p j h j -k h W j +t j h j / tanα=0 F j-1 -F j +(1+k v )W j +τ j h j -p j h j / tanα+t j h j =0 Among them, h j is the thickness of the jth soil strip; j is the strip number from top to bottom when the unit soil body (400) is horizontally divided into strips, 1≤j≤m, and its strip division method is consistent with the corresponding sliding soil wedge (300); σ j and τ j are the normal stress and tangential stress acting on the cantilever wall arm respectively; F j-1 and F j are the vertical inter-strip forces on the top and bottom surfaces of the j-th strip, respectively; W j is the deadweight of the j-th soil strip; l j-1 and l j is the length of the top and bottom of the jth block.

7. The method for calculating the earth pressure of the multi-stage cantilever wall stand as claimed in claim 6, characterized in that: In step 600, the calculation expression of the earth pressure resultant of each level of cantilever wall vertical arm is: Among them, E wk is the resultant earth pressure on the vertical arm of the k-th cantilever wall; m k is the total number of horizontal strips of the k-th unit soil (400).

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